Question: Gabriela is 16 years older than Jessica. Thirteen years ago, Gabriela was 3 times as old as Jessica. How old is Jessica now?
Answer: We can use the given information to write down two equations that describe the ages of Gabriela and Jessica. Let Gabriela's current age be $g$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $g = j + 16$ Thirteen years ago, Gabriela was $g - 13$ years old, and Jessica was $j - 13$ years old. The information in the second sentence can be expressed in the following equation: $g - 13 = 3(j - 13)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to use our first equation for $g$ and substitute it into our second equation. Our first equation is: $g = j + 16$ . Substituting this into our second equation, we get the equation: $(j + 16)$ $-$ $13 = 3(j - 13)$ which combines the information about $j$ from both of our original equations. Simplifying both sides of this equation, we get: $j + 3 = 3 j - 39$ Solving for $j$ , we get: $2 j = 42$ $j = 21$.